_f64_quad_gate.nx source

1// _f64_quad_gate.nx -- self-validating gate for the GAMS-H Simpson quadrature. 2// integral of f over [a,b] vs the EXACT closed-form value (free oracle): 3// int_0^1 x^2 = 1/3 ; int_0^(pi/2) sin = 1 ; int_0^1 e^x = e-1 ; int_1^2 1/x = ln2. 4// Reports the worst relative error; PASS iff max rel < 2^-29 (~1.9e-9, quadrature-grade). 5// Durable: QUADRATURE-GATE -> math_engine.log. license_tier: ORIGINAL 6import "nx_syscalls.nx" 7import "nx_f64.nx" 8import "nx_f64_div.nx" 9import "nx_f64_quad.nx" 10 11func qg_p(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 } 12func qg_f(fd: i64, s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(fd,s,n); return 0 } 13func qg_n(fd: i64, v: i64) -> i64 { let bb: *u8=sys_mmap(28); var m: i64=v; if m<0{m=0-m; sys_write(fd,"-" as *u8,1)}; let t: *u8=sys_mmap(28); var k: i64=0; if m==0{t[0]=48 as u8;k=1}; while m>0{t[k]=(48+(m%10)) as u8;m=m/10;k=k+1}; var i: i64=0; while i<k{bb[i]=t[k-1-i];i=i+1}; sys_write(fd,bb,k); return 0 } 14 15const QG_ZERO: i64 = 0 16const QG_ONE: i64 = 0x3FF0000000000000 17const QG_TWO: i64 = 0x4000000000000000 18const QG_THREE: i64 = 0x4008000000000000 19const QG_PIH: i64 = 0x3FF921FB54442D18 // pi/2 20const QG_E: i64 = 0x4005BF0A8B145769 // e 21const QG_LN2: i64 = 0x3FE62E42FEFA39EF // ln 2 22const QG_N: i64 = 500 23 24// |result - known| / |known| (returned as f64 bits) 25func qg_rel(result: i64, known: i64) -> i64 { 26 let d: i64 = nx_f64_sub(result, known) & 0x7FFFFFFFFFFFFFFF 27 let k: i64 = known & 0x7FFFFFFFFFFFFFFF 28 return nx_f64_div(d, k) 29} 30 31func main() -> i64 { 32 qg_p("=== F64-QUAD GATE: Simpson quadrature vs exact closed-form integrals ===\n" as *u8) 33 var maxrel: i64 = 0 34 // fid 0: int_0^1 x^2 = 1/3 35 let i0: i64 = nx_f64_quad_simpson(0, QG_ZERO, QG_ONE, QG_N) 36 let r0: i64 = qg_rel(i0, nx_f64_div(QG_ONE, QG_THREE)) 37 if r0 > maxrel { maxrel = r0 } 38 // fid 1: int_0^(pi/2) sin = 1 39 let i1: i64 = nx_f64_quad_simpson(1, QG_ZERO, QG_PIH, QG_N) 40 let r1: i64 = qg_rel(i1, QG_ONE) 41 if r1 > maxrel { maxrel = r1 } 42 // fid 2: int_0^1 e^x = e-1 43 let i2: i64 = nx_f64_quad_simpson(2, QG_ZERO, QG_ONE, QG_N) 44 let r2: i64 = qg_rel(i2, nx_f64_sub(QG_E, QG_ONE)) 45 if r2 > maxrel { maxrel = r2 } 46 // fid 3: int_1^2 1/x = ln2 47 let i3: i64 = nx_f64_quad_simpson(3, QG_ONE, QG_TWO, QG_N) 48 let r3: i64 = qg_rel(i3, QG_LN2) 49 if r3 > maxrel { maxrel = r3 } 50 51 let thr: i64 = 994 << 52 // 2^-29 ~ 1.9e-9 52 var ok: i64 = 0 53 if maxrel < thr { ok = 1 } 54 // worst-error bits -> approx neg-log2 (bits of accuracy) for the human line 55 let aexp: i64 = 1023 - (maxrel >> 52) 56 let lfd: i64 = sys_openat_append("knowledge/status/math_engine.log" as *u8, 0x1a4) 57 if lfd >= 0 { 58 qg_f(lfd, "QUADRATURE-GATE epoch=" as *u8); qg_n(lfd, sys_now_realtime_sec()) 59 qg_f(lfd, " fns=4 panels=" as *u8); qg_n(lfd, QG_N) 60 qg_f(lfd, " worst_rel_bits_of_accuracy=" as *u8); qg_n(lfd, aexp) 61 qg_f(lfd, " method=composite-simpson gams=H(quadrature)" as *u8) 62 if ok == 1 { qg_f(lfd, " verdict=GREEN\n" as *u8) } else { qg_f(lfd, " verdict=RED\n" as *u8) } 63 sys_close(lfd) 64 } 65 qg_p(" worst_rel_bits_of_accuracy=" as *u8); qg_n(1, aexp) 66 if ok == 1 { qg_p(" QUADRATURE-GATE: GREEN (GAMS-H integration class opened: Simpson vs exact integrals)\n" as *u8); sys_exit(0); return 0 } 67 qg_p(" QUADRATURE-GATE: RED (measured gap named)\n" as *u8) 68 sys_exit(1) 69 return 1 70}